Problem: $g(x)=9+4x$ $h(x)=\dfrac{x+21}{5}$ Write $(h\circ g)(x)$ as an expression in terms of $x$. $(h\circ g)(x)=$
Answer: First, let's write $(h\circ g)(x)$ as $h(g(x))$. Next, we write $g(x)$ as the input to function $h$. $h({g(x)})=\dfrac{{g(x)}+21}{5}$ Since $g(x)=9+4x$, this becomes: $\begin{aligned} h({g(x)})&=\dfrac{{9+4x}+21}{5}\\ \\ &=\dfrac{4x+30}{5}\\ \\ &=\dfrac{4}{5}x+6\\ \\ \end{aligned}$ Note: We simplified the result to obtain a nicer expression, but this is not necessary. The answer: $(h\circ g)(x)=\dfrac{4}{5}x+6$